Rapid heating and short annealing durations (of the order of several seconds) can be achieved using a dc electrical current [5-7] or infrared flash annealing of metallic glasses [8]. High heating rates and extremely fast annealing/crystallization are involved in the treatments by very short electrical pulses (10^-4 to 10^-3 s) of high current density (10⁷ to 10⁹ A m^-2) [9-12] and by lasers [13-15]. Rapid heating allows the metallic glass to crystallize at higher temperatures; certain crystallization stages can be bypassed. In recent years, thanks to the development of new laser experimental techniques, rapid heating of metallic glass became a part of the processes of laser-assisted amorphous coating deposition and additive manufacturing [15]. Up to date, the crystallization under pulsed heating has not been widely presented in the literature; however, recent studies show that unusual phenomena can occur when amorphous alloys are rapidly heated by a laser. LaGrange et al. [13] have shown that the kinetics of crystallization of amorphous films under extremely fast heating is very different from the kinetics observed under slow heating with nucleation and growth rates in the former case several orders of magnitude higher. In terms of microstructure, observations of the distinct features - spherulites in an amorphous matrix - locally forming under pulsed laser heating of pre-deposited powder layers are reported [15].

Electrical currents induce a variety of phenomena in amorphous materials [16-18] depending on the application mode. Due to Joule heating by the passing electrical current, metallic glass loses its thermal stability and crystallizes. As was suggested by Mizubayashi et al. [10], electrical current can induce a resonant collective motion of atoms, thereby enhancing atomic migration and facilitating crystallization at temperatures far below the crystallization temperature of the alloy.

where d is the density of the alloy; l is the length; s is the width and h is the thickness of the ribbon.

The Joule heat evolved during the pulse can be expressed as follows

The resistance of the ribbon piece can be estimated as

where ρ is the resistivity of the amorphous material measured to be 2.4 · 10^-6 Ω m.

The Joule heat evolved in the sample per unit mass is

The samples N1 to N4 in Table ​Table11 are placed in the order of increasing the maximum current density and the value of Joule heat per unit mass.

Ribbon N1 was thicker than the other samples and was set to experience the lowest current density. After the pulse, it retained its shape and did not show any visible cracks or macrodefects. On the other hand, samples N2, N3, and N4 became very brittle after electrical pulsing and contained a lot of cracks. The most severe effect was observed in sample N4. When even higher current densities were applied (not shown), the samples exploded, did not keep their wholeness and transformed into small pieces and powder particles.

XRD patterns of the crystallized ribbons are shown in Figure ​Figure11 along with the pattern of the initial ribbon. The as-quenched ribbon is amorphous as is confirmed by the presence of a broad halo in the pattern. In the pattern corresponding to sample N1, we observe a halo of reduced intensity and a very broad reflection from a crystalline phase TiCu₂, which indicates partial crystallization. Based on the shape of the XRD profile, one can anticipate the presence of very fine grains of the crystalline phase TiCu₂ (Amm2; a = 4.36 Å, b = 7.98 Å, c = 4.48 Å). Figure ​Figure2a2a shows an HRTEM image of the crystallized alloy that has experienced partial polymorphic crystallization and shows a two-phase structure with crystalline particles of 5 to 8 nm distributed in the residual amorphous matrix. A selected area diffraction pattern is shown in Figure ​Figure2b.2b. A larger area of the crystallized sample is shown in a dark-field image (Figure ​(Figure2c).2c). Similar microstructures can be obtained directly during casting of alloys of certain compositions [3] or can be produced through precisely controlled heating of initially amorphous alloys in in situ experiments using synchrotron radiation to detect the early formation of nanocrystals in an amorphous matrix [4].

The calculated Joule heat for ribbon N1 was enough only to increase the temperature of the material by 180 K from room temperature assuming the heat capacity of the Ti₃₃Cu₆₇ alloy C = 0.5·10³ J kg^-1 K^-1. According to Buschow [19] and Zaprianova et al. [20], the crystallization temperature of the Ti₃₃Cu₆₇ alloy is 700 K, which implies that during pulsing the crystallization temperature was not reached. Hence, non-thermal effects play an essential role in the crystallization processes. The crystallization of the alloy was induced by the electrical current, which is in agreement with observations of other authors [11,12]. Thus, Mizabayashi et al. [12] applied electrical pulses with a current density ranging between 1.7 · 10⁹ and 2.7 · 10⁹ A m^-2 to Zr₅₀Cu₅₀ amorphous ribbons triggering nanocrystallization in the sample that was not heated up to its crystallization temperature measured in the absence of current. In that case, plates of high thermal conductivity were put in contact with the ribbons during the experiment, based on which the authors considered the crystallization to be athermal and caused by electrical field only. In the present study, no special precautions were taken to dissipate heat from the sample while the current densities were of the order of 10⁹ A m^-2. However, it was possible to induce moderate heating and achieve partial crystallization due to the use of extremely short pulses. Also, as it will be seen below, there were a few areas in the sample, in which the temperature rose much higher than the calculated average value.

When higher current densities are applied to the samples, further crystallization stages are detected, as is seen from the XRD patterns of samples N2 to N4 (Figure ​(Figure1).1). The calculated values of Joule heat are also higher compared to that of sample N1. The amorphous halo is no longer detectable in the patterns of N3, while the TiCu₂ intermetallic phase decomposes to form intermetallic compounds indexed as Ti₂Cu₃ (P4/nmm; a = 3.13 Å, c = 13.95 Å) and TiCu₃ (Pmnm; a = 5.45 Å, b = 4.42 Å, c = 4.30 Å). A small amount of the amorphous phase may still be present in N2 and N4. The Joule heat evolved in ribbon N2 was enough to heat the alloy up to its solidus temperature, which is 1,123 K according to [21], and partially melt it; similar processes could be expected for ribbon N3. The calculations for ribbon N4 lead to a conclusion that the sample could fully melt and then re-crystallize. Indeed, N4 was very brittle and did not retain its shape after electrical pulsing. The crystal structure of the ribbons crystallized under electrical pulses differs from that of the ribbons crystallized by conventional annealing. Figure ​Figure33 shows an XRD pattern of the ribbon annealed in vacuum at 773 K for 15 min. The ribbon is fully crystallized and contains Ti₂Cu₃ (P4/nmm; a = 3.13 Å, c = 13.95 Å) and TiCu₃ (Pmmn; a = 5.16 Å, b = 4.35 Å, c = 4.53 Å) phases showing narrow reflections in the XRD pattern; the ratios of the XRD line intensities of the phases do not correspond to those of the ribbons crystallized by electrical pulsing. This leads to a conclusion that the crystal structure of the phases in the ribbons crystallized by pulsing is still metastable. Worth noting is the fact that the TiCu₃ phase formed during conventional annealing has lattice parameters different from those of the TiCu₃ phase formed during electrical pulsing (the phases were described using different JCPDS cards).

In order to reveal the microstructural features, the ribbons were electrochemically etched in a HNO₃-CH₃OH solution. Figure ​Figure44 shows a SEM image of the surface of the initial ribbon to be used as a reference when analyzing the structure of the crystallized ribbons shown in Figure ​Figure55 (two different magnifications in Figure ​Figure55 are shown for each sample in order to demonstrate unusual microstructural features and non-uniformity at different scales). A common feature of the crystallized ribbons was their non-uniform microstructure with regions that experienced local melting and rapid solidification. In N1, droplet-like featureless areas clearly indicate that melting and rapid solidification took place locally (Figure 5a,b). The surface of samples N2 (Figure 5c,d) and N3 (Figure 5e,f) subjected to electrical current is covered by a network of cracks. These features are more intense from sample N2 to N3 following the severity of electrical current conditions applied. In addition, droplet-like islands in N2 show that melting occurred in certain areas, manifesting thus a local temperature increase during the treatment of the samples by electrical pulsing. For comparison, the samples conventionally annealed and etched under the same conditions are shown in Figure 5g,h. They possess a perfectly uniform microstructure revealing micron and submicron grains of the crystallization products.

An explanation can be suggested in order to rationalize the observed microstructures of the ribbons crystallized under electrical current. Crystallization in amorphous ribbons starts in certain zones (first crystallized zones), which further determine the crystallization process and evolution of the microstructure [22]. Generally, these zones could be associated either with local compositional deviations increasing the likelihood of crystallization or with thickness variations and/or surface defects of the ribbons practically unavoidable during melt-spinning. In multicomponents metallic glasses, nanoscale compositional heterogeneities were predicted by Fujita et al. [23] using molecular dynamics simulation while mesoscale (submicron) heterogeneities were experimentally observed by Caron et al. [24]. In the present work, a binary metallic glass crystallizes and shows non-uniformities in the microstructure, whose scale is tens of microns. The surface of the initial amorphous ribbon etched under the same conditions as the crystallized ribbons reveals certain features that could appear as a result of the initial surface roughness of the as-spun ribbons. The scale of these features and their random distribution coincides with the scale and distribution of non-uniformities observed in the crystallized ribbons as droplet-like featureless areas. This allows us to draw a conclusion that the thickness variations and surface defects play a significant role in determining the behavior of the ribbons during crystallization under electrical current. The fact that the same ribbons when heated conventionally show a uniform microstructure clearly indicates that the observed non-uniformities formed as a response of the alloy ribbons to the passing electrical current. The as-spun ribbons are not ideally flat and the thinner areas of the ribbons are heated up to higher temperatures relative to the average temperature of the sample such that the alloy locally melts in the corresponding regions. The areas that crystallized first reduce their resistivity and at later stages evolve lower Joule heat compared to the regions that are still amorphous. This forms a non-uniform temperature field in the sample, which also rapidly changes in time as the parameters of the electrical current change during the pulse. The non-uniform temperature field in the samples creates mechanical stresses further contributing to the microstructural development in the crystallized sample. Since the pulses used in this work are very short, the non-uniform microstructures formed in the crystallized samples and metastable phase compositions are quenched and can be later observed at room temperature.

The scheme of the experimental set-up for applying electrical pulses to thin ribbons is shown in Figure ​Figure6.6. No special configuration was used to provide heat sink from the ribbon pieces subjected to electrical current. The length of the ribbon samples was 20 mm.

The XRD phase analysis of the initial and crystallized ribbons was performed using a D8 ADVANCE diffractometer (Bruker) using Cu Kα radiation.

In order to prepare samples for scanning electron microscopy (SEM) observations, the initial amorphous ribbon and the crystallized samples were electrochemically etched in a HNO3-CH3OH solution containing 33 vol.% of HNO₃ under an applied voltage of 5 V for 30 s. The SEM was performed using a Hitachi-Tabletop TM-1000 microscope (Japan).